The Cosmological Constant and Technical Naturalness
Sunny Itzhaki
hep-th/0604190 + work to appear
The CC problem used to be a simple problem
~
One loop
~ g
The CC problem used to be a simple problem… to state:
Why is the CC vanishing? The CC term is a relevant term that receives large quantum corrections:
Lorentz invariance + dim. analysis give
Cut off scale
The goal was to find a way to get 0.
The CC problem seems to have little to do with particle physics and more to do withdeep issues in quantum gravity.
• Old proposals to solve the CC problem:
1- Hawking’s wave function of the universe (most likely to have vanishing CC).
2- Coleman’s wormholes.
…
• Particle physics does not help much:
SUSY, that helps in a similar problem with the Higgs mass, gives at best
which is times larger than the total energy density in the universe.
604 10~)( TeV ~
6010
Now we are trying to explain a small and positive CC
•The bad news is that the CC problem evolved into three problems:
1- Why is the CC so small (in particle physics units)?
2- If so small why not zero?
3- Why now? Roughly when galaxies were formed the CC is of the order of the matter energy density in the universe.
• The bad news is that the CC problem evolved into three problems:
1- Why is the CC so small (in particle physics units)?
2- If so small why not zero?
3- Why now? Roughly when galaxies were formed the CC is of the order of the matter energy density in the universe.
• The good news is that we have a scale, to work with.
For example:
1- (…, Banks, …)
303 10~10 eV
Loop corrections to the CC are within the inflation range
In TeV SUSY theories the natural range of the vacuum energy is
Gauge mediation models Gravity mediation
Which is within the inflation range
• This assumption does not solve the CC problem, but if true it changes its nature:
CC and Inflation
The question is now: why is the ratio of the vacuum energy during inflationto the current vacuum energy so large and yet not infinite?
Why it is :
and not
Can be
The question is: why is the ratio of the vacuum energy during inflationto the current vacuum energy so large and yet not infinite?
Why it is :
and not
The good thing is that we have to do it only once:
Temperature driven phase transitions (like the EW or QCD)will not change the vacuum energy.
Out line
• Abbott’s model (85). The empty universe problem.
• The hep-th/0604190 model.
The cold universe problem.
• Solving the cold universe problem.
Abbott’s Model (85)
The action is
Instantons induce a potential:
When we have the symmetry
is technically natural. (similar to the mass of the electron)
• Small M is natural.
The renormalizedCC term
Also at the quantum level the potential looks like:
• In quantum mechanics the local minima are on equal footing.
• Here the situation is more interesting:
Hawking temperature in de-Sitter is .
• For in effect there are no local minima.
• For we have tunneling. The decay rate is Most of the time at small CC.
Regardless of we end up with a small CC
Regardless of we end up with a small CC
BUT we also end up with an empty universe.
This is known as the emptiness problem that appears also in other approaches tothe CC problem.
The hep-th/0604190 model
Let’s modify Abbott’s model in the following way:
The relaxation action is a simpler version of Abbott’s action
where .
Much like in Abbott’s case the vacuum energy is reduced slowly.
The challenge is to evade the emptiness problem by converting the potential energyinto kinetic energy.
is designed to fix that while making sure that the vacuum energy at the end of inflation is small.
That is makes
sure that we have
and not
We take
The potential is designed to have the following properties:
and
Now the dynamics is more interesting:
The effective mass is
Slow roll approximation.
(This is where it is important that )
Now the dynamics is more interesting:
The effective mass is
There is a phase transition: V
For
At the critical vacuum energy
an instability is developed and
acquires an expectation value.
The end result is a flat spacewith plenty of kinetic energy.
There are a couple of bounds on the we can get this way:
1- Energy conservation:
2- Vacuum energy can be converted to kinetic energy only when
the slow-roll approximation is not valid:
In our case (1) and (2) are the same so an upper bound on
is
What about quantum correction?
Claim:
The present value of the vacuum energy + Technical naturalness of the model ___________________________________
• The upper bound on the reheating temperature is at the TeV scale.
• SUSY is broken at around the TeV scale.
What about quantum correction?
Let’s consider the simplest potential
Quantum corrections to give non-vanishing vacuum energy, , that should be at most .
Because of the relevant term it is hard to control these quantum corrections without SUSY.
With SUSY we have
When SUSY is broken these corrections are enhanced:
• Gravity always mediates SUSY breaking from one sector to the other:
So the picture is:
Hidden sector
TeV SUSY
sector
Gravity mediation
(N) MSSM
Gauge mediation
Hidden sector
TeV SUSY
sector
Gravity mediation
(N) MSSM
Gauge mediation
So far we talked about: vacuum energy kinetic energy.
Hidden sector
TeV SUSY
sector
Gravity mediation
(N) MSSM
Gauge mediation
So far we talked about: vacuum energy kinetic energy.
we should have: vacuum energy kinetic energy SM heat.
Re-heating coupling
Can we re-heat without spoiling the naturalness of the model?
Direct approach:
Take
We need
BUT then:
A resolution:
Take instead
This includes
So
Looks like the exact same situation/problem as before.
But actually
So works fine.
Conclusion:
We have considered a model that:
• Appears to be consistent with basic exp. requirements (TeV SUSY and inflation).
• CC is technically natural.
Can the model be embedded in string theory?